When I use
$(LM)^\ast = (LM)^(0) \ucup (LM)^(1)\ucup (LM)^(2) $
I receive an error:
--this is a undefined control sequence
I need to use (LM)^*= (LM)^0 \ucap (LM)^1 \ucap..
and so on. How should I make it in LaTeX?
There is no symbol \ucup or \ucap; use \cup or \cap. Also, for superscripts (or subscripts that contain more than one token, brace them:

\documentclass{article}
\begin{document}
$(LM)^\ast = (LM)^{0} \cup (LM)^{1} \cup (LM)^{2}$
\end{document}
You can also find many other symbols in the Comprehensive LaTeX Symbol List.
\astor the\ucup? How about reading up on some basics. See What are good learning resources for a LaTeX beginner? Then, in order to find symbols and which packages they may belong to, read How to look up a symbol or identify a math symbol or character? – Werner Feb 04 '15 at 06:01